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Opposition control within the resolvent analysis framework

Luhar, M. and Sharma, A. S. and McKeon, B. J. (2014) Opposition control within the resolvent analysis framework. Journal of Fluid Mechanics, 749 . pp. 597-626. ISSN 0022-1120.

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This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi, Moin & Kim, J. Fluid Mech., vol. 262, 1994, pp. 75–110) as an example. Under this formulation, the velocity field for turbulent pipe flow is decomposed into a series of highly amplified (rank-1) response modes, identified from a gain analysis of the Fourier-transformed Navier– Stokes equations. These rank-1 velocity responses represent propagating structures of given streamwise/spanwise wavelength and temporal frequency, whose wall-normal footprint depends on the phase speed of the mode. Opposition control, introduced via the boundary condition on wall-normal velocity, affects the amplification characteristics (and wall-normal structure) of these response modes; a decrease in gain indicates mode suppression, which leads to a decrease in the drag contribution from that mode. With basic assumptions, this rank-1 model reproduces trends observed in previous direct numerical simulation and large eddy simulation, without requiring high-performance computing facilities. Further, a wavenumber–frequency breakdown of control explains the deterioration of opposition control performance with increasing sensor elevation and Reynolds number. It is shown that slower-moving modes localized near the wall (i.e. attached modes) are suppressed by opposition control. Faster-moving detached modes, which are more energetic at higher Reynolds number and more likely to be detected by sensors far from the wall, are further amplified. These faster-moving modes require a phase lag between sensor and actuator velocity for suppression. Thus, the effectiveness of opposition control is determined by a trade-off between the modes detected by the sensor. However, it may be possible to develop control strategies optimized for individual modes. A brief exploration of such mode-optimized control suggests the potential for significant performance improvement.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle
Sharma, A. S.0000-0002-7170-1627
McKeon, B. J.0000-0003-4220-1583
Additional Information:© 2014 Cambridge University Press. (Received 20 September 2013; revised 12 February 2014; accepted 12 April 2014; first published online 19 May 2014) This material is based on work supported by the Air Force Office of Scientific Research under award FA9550-12-1-0469 (program manager Dr Douglas Smith).
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0469
Subject Keywords:drag reduction; turbulence control; turbulent boundary layers
Record Number:CaltechAUTHORS:20140725-153829494
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Official Citation:M. Luhar, A. S. Sharma and B. J. McKeon (2014). Opposition control within the resolvent analysis framework. Journal of Fluid Mechanics, 749, pp 597-626 doi:10.1017/jfm.2014.209
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47506
Deposited By: Tony Diaz
Deposited On:25 Jul 2014 22:58
Last Modified:03 Oct 2019 06:54

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